Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <stdio.h>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#define rep(i,a,n) for(ll i =(a);i<(n);++i)
#define urep(i,a,n) for(ll i = (a);i>=(n);--i)
#define all(x) (x).begin(),(x).end()
#define INF 1e18
const int mod = 1e9 + 7;
typedef long long ll;
using namespace std;
ll dx[4] = { 1,-1,0,0 };
ll dy[4] = { 0,0,1,-1 };
ll N,M,X,Y,A,B,C,Q,K,R,W,H;
string S,T;
ll ans;
ll x[1000000];
ll y[1000000];
ll a[1000000];
ll b[1000000];
ll c[1000000];
ll t[1000000];
string s[10000];
ll gcd(ll a, ll b) {
	if (b == 0)return a;
	else return gcd(b, a%b);
}
struct Edge{
	ll to,cost;
	 Edge(int to, int cost) : to(to), cost(cost) {}
};
typedef vector<vector<Edge> > AdjList;
AdjList graph;
vector<ll> dist;
int main() {
	cin>>N;
	rep(i,0,N){
		cin>>a[i];
	}
	sort(a,a+N);
	double ans=0;
	rep(i,1,N-2){
		ans = max(ans,((double)(a[N-1]+a[N-2]))/((double)(a[i]-a[i-1])));
	}
	ans = max(ans,double(a[N-3]+a[N-4])/(double)(a[N-1]-a[N-2]));
	ans = max(ans,double(a[N-1]+a[N-4])/(double)(a[N-2]-a[N-3]));
	cout<<fixed<<ans<<endl;
	return 0;
}